Vertical Asymptotes: Occur when the denominator is zero, and the numerator is non-zero. Function approaches infinity. | Holes: Occur when both numerator and denominator are zero. Represent removable discontinuities.

1. Factor the numerator and denominator. 2. Identify zeros of the denominator. 3. Check if those zeros are also zeros of the numerator. 4. If a zero is only in the denominator, there's a vertical asymptote there.

1. Find the vertical asymptote. 2. Evaluate the one-sided limits as $x$ approaches the asymptote from the left and right. 3. Determine if the function approaches $\infty$ or $-\infty$ from each side.

1. Factor the numerator and denominator. 2. If a factor cancels out from both, there is a hole at the x-value that makes that factor zero.

1. Factor: $r(x) = \frac{(x-1)(x+1)}{(x-1)(x-1)}$. 2. Simplify: $r(x) = \frac{x+1}{x-1}$. 3. Vertical asymptote: $x=1$.

A vertical line that the graph of a function approaches but never touches, where the function's value goes to infinity (or negative infinity).

A function of the form $r(x) = \frac{p(x)}{q(x)}$, where $p(x)$ and $q(x)$ are polynomial functions.

The number of times its corresponding factor appears in the polynomial.

A point where both the numerator and denominator of a rational function are zero. It is a removable discontinuity.